%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:45 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 5 RR)
% Number of literals : 51 ( 50 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(f04,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(f01,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(f03,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(f07,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
cnf(f06,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(f05,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(goal,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_8,axiom,
rd(mult(X1,X1),X1) = X1,
f02 ).
cnf(c_0_9,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
f04 ).
cnf(c_0_10,axiom,
ld(X1,mult(X1,X1)) = X1,
f01 ).
cnf(c_0_11,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
f03 ).
cnf(c_0_12,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
f07 ).
cnf(c_0_14,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_9]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_18,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
f06 ).
cnf(c_0_19,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_9]),c_0_9]) ).
cnf(c_0_21,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_22,plain,
mult(rd(mult(X1,X2),ld(X3,X3)),ld(X3,X3)) = mult(X1,mult(rd(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_23,plain,
mult(rd(ld(X1,X1),X1),X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_19]) ).
cnf(c_0_24,plain,
mult(mult(rd(X1,ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_23]) ).
cnf(c_0_25,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_26,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_14]) ).
cnf(c_0_27,plain,
mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(rd(mult(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_28,plain,
mult(rd(mult(X1,ld(X2,X2)),X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_21]) ).
cnf(c_0_29,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_30,plain,
mult(X1,ld(ld(X2,X2),ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]),c_0_14]) ).
cnf(c_0_31,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_32,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_31]),c_0_14]) ).
cnf(c_0_33,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_22]),c_0_27]) ).
cnf(c_0_34,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
f05 ).
cnf(c_0_35,plain,
mult(X1,mult(rd(X2,rd(X3,X4)),rd(X3,X4))) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_36,plain,
mult(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(rd(X1,X2),X2),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_37,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_11]),c_0_11]) ).
cnf(c_0_38,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_39,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_14]),c_0_9]) ).
cnf(c_0_40,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_37,c_0_11]) ).
cnf(c_0_41,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_42,plain,
mult(rd(X1,mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(rd(X1,X3),X3),
inference(spm,[status(thm)],[c_0_38,c_0_9]) ).
cnf(c_0_43,plain,
mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_16]),c_0_19]) ).
cnf(c_0_44,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_40,c_0_14]) ).
cnf(c_0_45,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
c_0_41 ).
cnf(c_0_46,plain,
mult(rd(X1,mult(X2,X3)),mult(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_9]),c_0_39]),c_0_39]) ).
cnf(c_0_47,plain,
mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_21]) ).
cnf(c_0_48,negated_conjecture,
mult(rd(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_9]),c_0_9]) ).
cnf(c_0_49,plain,
mult(rd(X1,ld(X2,X3)),ld(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_46]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:34:08 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.61 % Version: 3.5.1
% 0.27/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.61 % Starting sh5l with 300s (1) cores
% 0.27/0.61 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3561374 completed with status 0
% 0.27/0.61 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.27/0.61 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.61 % No SInE strategy applied
% 0.27/0.61 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.27/0.61 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.61 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.27/0.61 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.27/0.61 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.27/0.62 % Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.27/0.62 % U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3561383 completed with status 0
% 0.27/0.62 % Result found by U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.27/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.27/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.62 % No SInE strategy applied
% 0.27/0.62 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.27/0.62 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.27/0.62 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.27/0.62 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.27/0.62 % Preprocessing time : 0.002 s
% 0.27/0.62 % Presaturation interreduction done
% 0.27/0.62
% 0.27/0.62 % Proof found!
% 0.27/0.62 % SZS status Unsatisfiable
% 0.27/0.62 % SZS output start CNFRefutation
% See solution above
% 0.27/0.62 % Parsed axioms : 8
% 0.27/0.62 % Removed by relevancy pruning/SinE : 0
% 0.27/0.62 % Initial clauses : 8
% 0.27/0.62 % Removed in clause preprocessing : 0
% 0.27/0.62 % Initial clauses in saturation : 8
% 0.27/0.62 % Processed clauses : 172
% 0.27/0.62 % ...of these trivial : 46
% 0.27/0.62 % ...subsumed : 0
% 0.27/0.62 % ...remaining for further processing : 126
% 0.27/0.62 % Other redundant clauses eliminated : 0
% 0.27/0.62 % Clauses deleted for lack of memory : 0
% 0.27/0.62 % Backward-subsumed : 0
% 0.27/0.62 % Backward-rewritten : 75
% 0.27/0.62 % Generated clauses : 3359
% 0.27/0.62 % ...of the previous two non-redundant : 2269
% 0.27/0.62 % ...aggressively subsumed : 0
% 0.27/0.62 % Contextual simplify-reflections : 0
% 0.27/0.62 % Paramodulations : 3359
% 0.27/0.62 % Factorizations : 0
% 0.27/0.62 % NegExts : 0
% 0.27/0.62 % Equation resolutions : 0
% 0.27/0.62 % Disequality decompositions : 0
% 0.27/0.62 % Total rewrite steps : 3624
% 0.27/0.62 % ...of those cached : 2535
% 0.27/0.62 % Propositional unsat checks : 0
% 0.27/0.62 % Propositional check models : 0
% 0.27/0.62 % Propositional check unsatisfiable : 0
% 0.27/0.62 % Propositional clauses : 0
% 0.27/0.62 % Propositional clauses after purity: 0
% 0.27/0.62 % Propositional unsat core size : 0
% 0.27/0.62 % Propositional preprocessing time : 0.000
% 0.27/0.62 % Propositional encoding time : 0.000
% 0.27/0.62 % Propositional solver time : 0.000
% 0.27/0.62 % Success case prop preproc time : 0.000
% 0.27/0.62 % Success case prop encoding time : 0.000
% 0.27/0.62 % Success case prop solver time : 0.000
% 0.27/0.62 % Current number of processed clauses : 43
% 0.27/0.62 % Positive orientable unit clauses : 43
% 0.27/0.62 % Positive unorientable unit clauses: 0
% 0.27/0.62 % Negative unit clauses : 0
% 0.27/0.62 % Non-unit-clauses : 0
% 0.27/0.62 % Current number of unprocessed clauses: 2006
% 0.27/0.62 % ...number of literals in the above : 2006
% 0.27/0.62 % Current number of archived formulas : 0
% 0.27/0.62 % Current number of archived clauses : 83
% 0.27/0.62 % Clause-clause subsumption calls (NU) : 0
% 0.27/0.62 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.62 % Non-unit clause-clause subsumptions : 0
% 0.27/0.62 % Unit Clause-clause subsumption calls : 9
% 0.27/0.62 % Rewrite failures with RHS unbound : 0
% 0.27/0.62 % BW rewrite match attempts : 333
% 0.27/0.62 % BW rewrite match successes : 97
% 0.27/0.62 % Condensation attempts : 0
% 0.27/0.62 % Condensation successes : 0
% 0.27/0.62 % Termbank termtop insertions : 41947
% 0.27/0.62 % Search garbage collected termcells : 2
% 0.27/0.62
% 0.27/0.62 % -------------------------------------------------
% 0.27/0.62 % User time : 0.078 s
% 0.27/0.62 % System time : 0.006 s
% 0.27/0.62 % Total time : 0.084 s
% 0.27/0.62 % Maximum resident set size: 3632 pages
% 0.27/0.62
% 0.27/0.62 % -------------------------------------------------
% 0.27/0.62 % User time : 0.361 s
% 0.27/0.62 % System time : 0.036 s
% 0.27/0.62 % Total time : 0.398 s
% 0.27/0.62 % Maximum resident set size: 4608 pages
% 0.27/0.62 % E exiting
%------------------------------------------------------------------------------